解决百亿级向量搜索中因几何失配导致的性能下降问题
MCGI: Manifold-Consistent Graph Indexing for Billion-Scale Disk-Resident Vector Search
- 基于局部内在维数动态调整搜索范围，适应数据真实几何结构
- 在五个亿级数据集上优于五种主流基线方法，精度与效率双提升
- 适合需要高维向量高效检索的大规模应用，如推荐系统、图像搜索
基于图的近似最近邻（ANN）搜索在高维空间中常因欧氏距离与测地距离不匹配而性能下降，导致贪婪路由偏离数据流形。本文提出流形一致图索引（MCGI），一种几何感知且支持磁盘驻留的索引方法，利用局部内在维数（LID）动态适应数据的内在几何结构。与传统算法均匀处理各维度不同，MCGI根据就地几何分析调节其束搜索预算，用一个几何相关的区间替代单一标量参数，显著降低对数据特定超参数的敏感性，在不同维度数据集间保持稳定。理论分析表明，MCGI通过保持流形一致的拓扑连通性，提供稳健的近似结果。在五个亿级规模数据集上，对比五种工业标准基线的大量实验验证了该方法的优势。
原文摘要 · Abstract (English)
Graph-based Approximate Nearest Neighbor (ANN) search often suffers from performance degradation in high-dimensional spaces due to the Euclidean-Geodesic mismatch, where greedy routing diverges from the underlying data manifold. To address this challenge, this paper presents Manifold-Consistent Graph Indexing (MCGI), a geometry-aware and disk-resident indexing method that leverages Local Intrinsic Dimensionality (LID) to dynamically adapt search strategies to the intrinsic geometry of data. Unlike conventional algorithms that treat dimensions uniformly, MCGI modulates its beam search budget based on in-situ geometric analysis, which reduces sensitivity to data-specific hyperparameters by replacing a single scalar with a geometry-informed range that remains stable across datasets of varying dimensionality. Theoretical analysis demonstrates that MCGI provides robust approximation by preserving manifold-consistent topological connectivity. Extensive evaluations against five industry-standard baselines across five datasets up to billion scales confirm the advantages of the proposed approach.
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